Related papers: Beyond Flatland: A Geometric Take on Matching Meth…

Manifolds discovered by machine learning models provide a compact representation of the underlying data. Geodesics on these manifolds define locally length-minimising curves and provide a notion of distance, which are key for reduced-order…

We study nonparametric distance-based (isotropic) local polynomial methods for estimating the boundary average treatment effect curve, a causal functional that captures treatment effect heterogeneity in boundary discontinuity designs. We…

Recently, many researchers have advanced data-driven methods for modeling heterogeneous treatment effects (HTEs). Even still, estimation of HTEs is a difficult task -- these methods frequently over- or under-estimate the treatment effects,…

The techniques and analysis presented in this thesis provide new methods to solve optimization problems posed on Riemannian manifolds. These methods are applied to the subspace tracking problem found in adaptive signal processing and…

Neural models learn representations of high-dimensional data on low-dimensional manifolds. Multiple factors, including stochasticities in the training process, model architectures, and additional inductive biases, may induce different…

Observational studies provide invaluable opportunities to draw causal inference, but they may suffer from biases due to pretreatment difference between treated and control units. Matching is a popular approach to reduce observed covariate…

Low-dimensional embeddings for data from disparate sources play critical roles in multi-modal machine learning, multimedia information retrieval, and bioinformatics. In this paper, we propose a supervised dimensionality reduction method…

Matching promises transparent causal inferences for observational data, making it an intuitive approach for many applications. In practice, however, standard matching methods often perform poorly compared to modern approaches such as…

The study of causal effects in the presence of unmeasured spatially varying confounders has garnered increasing attention. However, a general framework for identifiability, which is critical for reliable causal inference from observational…

In computer vision and medical imaging, the problem of matching structures finds numerous applications from automatic annotation to data reconstruction. The data however, while corresponding to the same anatomy, are often very different in…

Many rare diseases offer limited established treatment options, leading patients to switch therapies when new medications emerge. To analyze the impact of such treatment switches within the low sample size limitations of rare disease…

Existing weighting methods for treatment effect estimation are often built upon the idea of propensity scores or covariate balance. They usually impose strong assumptions on treatment assignment or outcome model to obtain unbiased…

Machine learning holds tremendous promise for transforming the fundamental practice of scientific discovery by virtue of its data-driven nature. With the ever-increasing stream of research data collection, it would be appealing to…

Recently, there has been great interest in estimating the conditional average treatment effect using flexible machine learning methods. However, in practice, investigators often have working hypotheses about effect heterogeneity across…

Background: Pairwise and network meta-analyses using fixed effect and random effects models are commonly applied to synthesise evidence from randomised controlled trials. The models differ in their assumptions and the interpretation of the…

In most computer vision and image analysis problems, it is necessary to define a similarity measure between two or more different objects or images. Template matching is a classic and fundamental method used to score similarities between…

Randomization, as a key technique in clinical trials, can eliminate sources of bias and produce comparable treatment groups. In randomized experiments, the treatment effect is a parameter of general interest. Researchers have explored the…

Joint modeling of spatially-oriented dependent variables is commonplace in the environmental sciences, where scientists seek to estimate the relationships among a set of environmental outcomes accounting for dependence among these outcomes…

We propose an approach for capturing the signal variability in hyperspectral imagery using the framework of the Grassmann manifold. Labeled points from each class are sampled and used to form abstract points on the Grassmannian. The…

It is often of interest to infer lower-dimensional structure underlying complex data. As a flexible class of non-linear structures, it is common to focus on Riemannian manifolds. Most existing manifold learning algorithms replace the…